We consider a minmax feedback control problem for a linear dynamic system with a positional quality criterion, which is the norm of the set of deviations of the motion from given target points at given times. The problem is formalized as a positional differential game. A numerical method is given for finding an approximate value of the game and constructing an optimal (minmax and maxmin) control law. The method is based on the recursive construction of upper convex (concave) hulls of auxiliary program functions. In addition, we use the "pixel" approximation of the domains of convexified functions and the approximate construction of the upper convex hull of a function as the lower envelope of a finite set of support hyperplanes of its subgraph.